递归可列实数的部分随机性的等价刻画
Equivalent characterizations of partial randomness for a recursively enumerable real
摘要：
一个实数α称为递归可逼近的，如果存在一个可计算的、递增的有理数序列收敛于α。一个递归可重算实数α的随机性可以用以下几个概念来描述：程序大小复杂度、马丁-勒夫检验、蔡廷的Ω数、α的控制性和Ω相似性、可计算的、递增的有理数序列收敛到α的普适性，以及普适概率。在本文中，我们推广了这些随机性的部分随机性的概念，参数化的概念以上的每一个实数T \in（0，1]。因此，我们提出了几个等价的部分随机性的递归可列实数的特征。
英文摘要：
A real number αis called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to α. The randomness of a recursively enumerable real αcan be characterized in various ways using each of the notions; program-size complexity, Martin-Löf test, Chaitin's Ωnumber, the domination and Ω-likeness of α, the universality of a computable, increasing sequence of rational numbers which converges to α, and universal probability. In this paper, we generalize these characterizations of randomness over the notion of partial randomness by parameterizing each of the notions above by a real number T\in(0,1]. We thus present several equivalent characterizations of partial randomness for a recursively enumerable real number.
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